Most county clerks will record various agreements upon request. Texas does not have a pro-forma for RDPs, so you would have to have it drawn up -- preferably by an attorney after each consulting with your OWN attorneys -- and the Harris County Recorder's office could record it as a matter of public record. Would they, is another matter entirely.
The State of Texas does not recognize the concept of registered domestic partnerships, either same sex or opposite sex, and leaves it to each county to decide. As far as I can tell, only Travis County (Austin, Lakeway and Lago Vista -- filthy liberals) formally recognizes RDPs.
The only other option anywhere else in TX that has any legal meaning would be to declare yourselves a common law married couple and file that declaration with Harris County. TX does recognize common law marriages but requires that they are recorded by the county recorder in order to avoid any "surprise" or unintentional common law marriages.
From a federal income tax perspective, an RDP is meaningless. Your income tax filing status would not change.
What would be affected would be the tax free status of any health insurance premiums paid for your coverage. Unless you are your g/f's dependent for federal tax purposes, any company contribution towards your coverage is taxable income to her. Also, any premiums that she pays for your coverage cannot be excluded from her taxable income. So basically the entire cost of your health insurance becomes taxable income to her.
To be claimed as her dependent on her return requires that your gross income is less than the personal exemption amount ($3,900 for 2013), you reside in her home for the entire year, and she provides more than half of your total support for the year. There must also not be any laws or ordinances that bar cohabitation of unmarried persons, even if such laws or ordinances are unenforced.